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Applied Optics

Quantum-noise-limited interferometric phase measurements

Andrew J. Stevenson, Malcolm B. Gray, Hans‐A. Bachor, David E. McClelland

Published Jul 1, 1993• 44 citations
Publisher

Abstract

Two schemes for interferometric optical phase measurement, with sensitivity limited only by quantum noise in the light, are analyzed. Direct detection is applicable to signals at modulation frequencies away from the technical noise of the light, so that quantum noise dominates the measurement. Alternatively signals otherwise obscured by classical optical noise may be recovered with a phase-modulation technique that shifts the signals to a quantum-noise-limited region of the photocurrent spectrum. The analysis is tested experimentally by using a polarimetric electric-field sensor. In the direct-detection scheme quantum-noise-limited performance produced a phase sensitivity of 0.25 µrad. The indirect scheme allowed subkilohertz signals to be extracted from classical noise 67 dB greater with sensitivity approaching the quantum noise limit.

DOI
10.1364/ao.32.003481

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Quantum noise limited interferometry for subhertz phase measurement is of essence in precision metrology applications, such as gravitational wave detection. However, suppression of subhertz classical noises below the shot-noise level is very challenging in practice. Two-frequency interferometry has been previously proposed to avoid low-frequency noises and may be useful for squeezing-enhanced high-precision phase measurement. Here we experimentally demonstrate a subhertz interferometer at the standard quantum noise (shot-noise) limit, by use of dual-frequency coherent probe light at the input and phase-sensitive heterodyne detection to measure the output interfered light. When the interferometer is locked at a dark fringe, the noise floor of the phase variance in the interferometer reaches the shot-noise level down to Fourier frequencies below 1 Hz. This work should pave a way for a realization of subhertz interferometry beyond the shot-noise limit.

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Two schemes for interferometric optical phase measurement, with sensitivity limited only by quantum noise in the light, are analyzed. Direct detection is applicable to signals at modulation frequencies away from the technical noise of the light, so that quantum noise dominates the measurement. Alternatively signals otherwise obscured by classical optical noise may be recovered with a phase-modulation technique that shifts the signals to a quantum-noise-limited region of the photocurrent spectrum. The analysis is tested experimentally by using a polarimetric electric-field sensor. In the direct-detection scheme quantum-noise-limited performance produced a phase sensitivity of 0.25 µrad. The indirect scheme allowed subkilohertz signals to be extracted from classical noise 67 dB greater with sensitivity approaching the quantum noise limit.
Interferometric detection of gravitational waves at levels of astrophysical interest is expected to require measurement of optical phase differences of $\ensuremath{\le}{10}^{\ensuremath{-}10}$ rad. To achieve this sensitivity the measurement must be made at the quantum (shot noise) limit. We have built a laboratory-scale interferometer to investigate limits to sensing the phase at this level, and obtained, with 70 W of circulating power, a phase sensitivity limited by shot noise of $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\phantom{\rule{0ex}{0ex}}\mathrm{rad}/\sqrt{\mathrm{Hz}}$ at frequencies above 1.5 kHz. We describe the experiment and discuss the implications for the Laser Interferometer Gravitational-Wave Observatory (LIGO).
Interferometric detection of gravitational waves at a level of astrophysical interest is expected to require measurement of optical phase differences of < or = 10(-10) rad. A fundamental limit to the phase sensing is the statistics of photon detection--Poisson statistics for light in a coherent state. We have built a laboratory-scale interferometer to achieve and investigate the phase detection sensitivity required for the Laser Interferometer Gravitational-Wave Observatory. With 70 W of circulating power, we have obtained a phase sensitivity of 1.28 x 10(-10) rad/square root(Hz) at frequencies above 600 Hz, limited by quantum noise. Below 600 Hz, excess noise above the quantum limit is seen, and we present our investigations into the sources of this excess. Compared with the results of previous such experiments, the phase sensitivity over the full 100-Hz-10-kHz band of interest has been improved by factors of up to 100, with a factor-of-2.5 improvement in the quantum-limited level.
An interferometric detection scheme to measure optical phase shift with sensitivity beyond the shot noise limit is proposed. The theoretical calculation shows that using the quantum correlated twin beams produced from an optical parametric amplifier as the input fields of a Mach-Zehnder interferometer, the minimum detectable phase shift will exceed the shot noise limit N-1/2 and approach the Heisenberg limit N-1. The parametric dependences of the minimum detectable phase shift on the nonlinear interaction, input photon number, and detection efficiency are shown.
Optical quantum metrology uses specially-prepared states of light to probe sensitive samples. Choosing a suitable probe state allows one to extract more information per probe photon about an unknown parameter than is possible using any classical technique. In effect, these techniques improve the sensitivity of the measurement whenever the number of probe photons is constrained in some way. This thesis presents experimental and theoretical results on the use of pairs of time-frequency entangled photons in precision measurements. It begins with an overview of necessary background knowledge about quantum optics and quantum information. This is followed by a theoretical discussion on the estimation of a single delay using two-photon interference. We show that constraints on the probe photon's bandwidth complicate the measurement problem, requiring suitable optimization of the two-photon quantum state to avoid losing precision. We then consider the use of two-photon interference for linear spectroscopic measurements. Linear spectroscopy relates the absorption and phase spectrum of a sample to unknown electronic parameters. We describe a proof-of-principle experiment demonstrating that two-photon interferometric spectroscopy can be used for simultaneously measurement of both absorption and phase. This is followed by an information-theoretic discussion of the precision of this technique. For low losses, we show that the method provides phase sensitivity similar to classical interferometry while approaching the optimal absorption precision of any possible measurement. If the absorption and phase values are both related to a single unknown parameter, then our technique provides improved sensitivity to this parameter compared to both classical measurements and other quantum techniques in the presence of realistic levels of loss. We conclude with a discussion of quantum-optical coherence tomography, which is a two-photon interferometric method for determining the material structure of a sample. We present an ongoing experiment which aims to apply the method to tissue-like samples, where the quantum measurement is limited by a poor signal-to-noise ratio. Preliminary results demonstrate that this noise can be largely reduced by suitable frequency-domain filtering. This allows us to precisely determine the position of a scattering center using a few hundred detected photon pairs despite the presence of large amounts of noise. We follow this with a theoretical discussion of signal artifacts which are known to complicate the measured interferogram. We show these artifacts are due to a distinct interferometric effect, which can be distinguished from the signal of interest using the relative time delay between detected photons. We conclude with a brief discussion on possible techniques for artifact removal.
A Mach-Zehnder interferometer (MZI) provides an effective interferometric readout approach for enhancing the performance of Rydberg-atom-based microwave electric-field sensing. The phase tuning based on a piezoelectric transducer (PZT) relies on mechanical path length modulation, which can limit phase precision, modulation frequency, and the level of system integration. Here, we demonstrate a fiber-integrated MZI architecture in which the interferometric phase is controlled electronically by a pair of double-pass acousto-optic modulators (AOMs). The additional propagation phase accumulated by the frequency-shifted light in an optical fiber enables continuous tuning of the relative phase between the two interferometer arms over a fixed optical path, without using moving components. A frequency adjustment Δf = 9.463 MHz produces a full 2π phase shift, confirming the reproducibility and continuous tunability of the method, with an experimentally measured phase stability at the milliradian level. Based on this interferometric readout, we implement a Rydberg-atom-based microwave electric-field measurement scheme in a room-temperature cesium vapor cell. At the optimized absorption-dominated operating point of Δϕ = π, corresponding to an AOM driving frequency of 93.9 MHz, the interferometric readout improves the measured signal-to-noise ratio by about 4 dB compared with the non-interferometric case. The directly measured electric-field sensitivity at the position of the cesium vapor cell is 4.2×10-6V/m/Hz. Compared with PZT-based schemes, this approach improves interferometric stability and tuning precision, and provides better compatibility with compact and integrated implementations.
Quantum noise limited interferometry for subhertz phase measurement is of essence in precision metrology applications, such as gravitational wave detection. However, suppression of subhertz classical noises below the shot-noise level is very challenging in practice. Two-frequency interferometry has been previously proposed to avoid low-frequency noises and may be useful for squeezing-enhanced high-precision phase measurement. Here we experimentally demonstrate a subhertz interferometer at the standard quantum noise (shot-noise) limit, by use of dual-frequency coherent probe light at the input and phase-sensitive heterodyne detection to measure the output interfered light. When the interferometer is locked at a dark fringe, the noise floor of the phase variance in the interferometer reaches the shot-noise level down to Fourier frequencies below 1 Hz. This work should pave a way for a realization of subhertz interferometry beyond the shot-noise limit.